Eigen Microstate Condensation and Critical Phenomena in the Lennard-Jones Fluid
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866909991944847360 |
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| author | Yang, Lan Pang, Zhaorong Qiao, Chongzhi Hu, Gaoke Dong, Jiaqi Shi, Rui Chen, Xiaosong |
| author_facet | Yang, Lan Pang, Zhaorong Qiao, Chongzhi Hu, Gaoke Dong, Jiaqi Shi, Rui Chen, Xiaosong |
| contents | Despite extensive study of the liquid-gas phase transition, accurately determining the critical point and the critical exponents in fluid systems through direct simulation remains a challenge. We employ the eigen microstate theory (EMT) to investigate the liquid-gas continuous phase transition in the Lennard-Jones (LJ) fluid within the canonical ensemble. In EMT, the probability amplitudes of eigen microstates serve as the order parameter. Using finite-size scaling of probability amplitudes, we simultaneously determine the critical temperature, $T_c = 1.188(2)$, and critical density, $ρ_c = 0.320(4)$. Furturemore, we obtain critical exponents of the LJ fluid, $β= 0.32(2)$ and $ν= 0.64(3)$, which demonstrate a great agreement with the Ising universality class. This method also reveals the mesoscopic structure of the emergent phase, characterizing the three-dimensional (3D) spatial configuration of the fluid in the critical region. This work also confirms the finite-size scaling behavior of the probability amplitudes of the eigen microstates in the critical region. The EMT provides a powerful tool for studying the critical phenomena of complex fluid system. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_10741 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Eigen Microstate Condensation and Critical Phenomena in the Lennard-Jones Fluid Yang, Lan Pang, Zhaorong Qiao, Chongzhi Hu, Gaoke Dong, Jiaqi Shi, Rui Chen, Xiaosong Statistical Mechanics Data Analysis, Statistics and Probability Despite extensive study of the liquid-gas phase transition, accurately determining the critical point and the critical exponents in fluid systems through direct simulation remains a challenge. We employ the eigen microstate theory (EMT) to investigate the liquid-gas continuous phase transition in the Lennard-Jones (LJ) fluid within the canonical ensemble. In EMT, the probability amplitudes of eigen microstates serve as the order parameter. Using finite-size scaling of probability amplitudes, we simultaneously determine the critical temperature, $T_c = 1.188(2)$, and critical density, $ρ_c = 0.320(4)$. Furturemore, we obtain critical exponents of the LJ fluid, $β= 0.32(2)$ and $ν= 0.64(3)$, which demonstrate a great agreement with the Ising universality class. This method also reveals the mesoscopic structure of the emergent phase, characterizing the three-dimensional (3D) spatial configuration of the fluid in the critical region. This work also confirms the finite-size scaling behavior of the probability amplitudes of the eigen microstates in the critical region. The EMT provides a powerful tool for studying the critical phenomena of complex fluid system. |
| title | Eigen Microstate Condensation and Critical Phenomena in the Lennard-Jones Fluid |
| topic | Statistical Mechanics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2601.10741 |